Speed and Velocity: Difference between revisions
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Unit vectors are also closely related to velocity and speed. Basically a unit vector is an arrow with a magnitude of 1 unit that points in the direction of a given vector. Unit vectors can be used to switch between speed and velocity. | Unit vectors are also closely related to velocity and speed. Basically a unit vector is an arrow with a magnitude of 1 unit that points in the direction of a given vector. Unit vectors can be used to switch between speed and velocity. | ||
The equation to find the unit vector of velocity is as follows | |||
[[File:uniteq.JPG]] | |||
=Simple Examples= | =Simple Examples= | ||
Revision as of 15:22, 30 November 2015
by Matt Schoonover
Speed and Velocity
Speed and velocity are used fairly interchangeably in casual conversation, but when it comes to physics the two can mean vastly different things. Velocity has direction and therefor a vector quantity. Speed is the scalar form of velocity and therefor has no direction.
The most basic equation for velocity is
From this comes the average velocity equation of
The equation for speed is
A Mathematical Model
In order to find the velocity of an object one must find the change in distance over the change in time. In order to find the speed of an object one must find the magnitude of the velocity. Both are measured in meters per second.
A Computational Model
To help demonstrate the difference between the two, I wrote some simple code to model the motion of a ball moving on a track.
In the first picture, the velocity is only in one direction, so the speed and velocity are the same.
However, in the second picture, the velocity is in the x and y direction, so the speed and velocity are not the same.
Unit Vectors
Unit vectors are also closely related to velocity and speed. Basically a unit vector is an arrow with a magnitude of 1 unit that points in the direction of a given vector. Unit vectors can be used to switch between speed and velocity.
The equation to find the unit vector of velocity is as follows
Simple Examples
1. If a person walked a distance of 10 meters in 5 seconds, what is their average velocity?
Solution: Using the average velocity equation will tell you that the answer is 2 m/s.
2. If someone traveled with a velocity of 13 m/s for 3 minutes, how far would they have traveled?
Solution: First convert 3 minutes to seconds(180). Then use the velocity equation to solve for distance. You should get 2,340 m.
Connectedness
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See also
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Further reading
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